Apollonius <Pergaeus>, Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

Table of contents

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[81.] PROPOSITIO LX.
Page: 100 (62)
[82.] PROPOSITIO LXI.
Page: 100 (62)
[83.] Notæ in Propoſit. LVIII.
Page: 101 (63)
[84.] Notæ in Propoſit. LIX. LXII. & LXIII.
Page: 102 (64)
[85.] Notæ in Propoſit. LX.
Page: 103 (65)
[86.] Notæ in Propoſit. LXI.
Page: 103 (65)
[87.] SECTIO DECIMA Continens Propof. XXXXIV. XXXXV. Apollonij.
Page: 105 (67)
[88.] PROPOSITIO XXXXIV.
Page: 105 (67)
[89.] PROPOSITIO XXXXV.
Page: 106 (68)
[90.] Notæ in Propoſ. XXXXIV.
Page: 106 (68)
[91.] Notæ in Propoſ. XLV.
Page: 107 (69)
[92.] SECTIO VNDECIMA Continens Propoſ. LXVIII. LXIX. LXX. & LXXI. Apollonij. PROPOSITIO LXVIII. LXIX.
Page: 108 (70)
[93.] PROPOSITIO LXX.
Page: 109 (71)
[94.] PROPOSITIO LXXI.
Page: 109 (71)
[95.] Notæ in Propoſit. LXVIII. LXIX. LXX. & LXXI.
Page: 109 (71)
[96.] SECTIO DVODECIMA Continens XXIX. XXX. XXXI. Propoſ. Appollonij.
Page: 110 (72)
[97.] Notæ in Propoſit. XXIX. XXX. & XXXI.
Page: 111 (73)
[98.] SECTIO DECIMATERTIA Continens Propoſ. LXIV. LXV. LXVI. LXVII. & LXXII. Apollonij. PROPOSITIO LXIV. LXV.
Page: 112 (74)
[99.] PROPOSITIO LXVI.
Page: 113 (75)
[100.] PROPOSITIO LXVII.
Page: 114 (76)
[101.] PROPOSITIO LXXII.
Page: 115 (77)
[102.] MONITVM.
Page: 116 (78)
[103.] LEMMA IX.
Page: 116 (78)
[104.] LEMMA X.
Page: 116 (78)
[105.] LEMMA XI.
Page: 117 (79)
[106.] Notæ in Propoſ. LXIV. & LXV.
Page: 117 (79)
[107.] Notæ in Propoſ. LXVI.
Page: 120 (82)
[108.] Ex demonſtratione præmiſſa propoſitionum 64. & 65. deduci poteſt conſectarium, à quo notæ ſubſe-quentes breuiores reddantur. COROLLARIVM PROPOSIT. LXIV. & LXV.
Page: 120 (82)
[109.] Notæ in Propoſ. LXVII.
Page: 121 (83)
[110.] COROLLARIVM PROPOSIT. LXVII.
Page: 122 (84)
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              <pb o="15" file="0053" n="53" rhead="Conicor. Lib. V."/>
            A B ad B F eſt, vt D E ad E H; </s>
            <s xml:id="echoid-s1158" xml:space="preserve">ergo A B ad A F eſt, vt E D ad D H; </s>
            <s xml:id="echoid-s1159" xml:space="preserve">ſed B A
              <lb/>
            ad maiorem C A habet minorem proportionem quàm ad F A; </s>
            <s xml:id="echoid-s1160" xml:space="preserve">igitur B A ad A C
              <lb/>
            minorem proportionem habet quàm E D ad D H.</s>
            <s xml:id="echoid-s1161" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s1162" xml:space="preserve">Septimò, dico è contra, quod comparando differentias terminorum ad ante-
              <lb/>
            cedentes C A ad A B maiorem proportionem habebit quàm H D ad D E. </s>
            <s xml:id="echoid-s1163" xml:space="preserve">Quo-
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            niam, ex præcedenti caſu, B A ad A C minorem proportionem habebat quàm E
              <lb/>
            D ad D H; </s>
            <s xml:id="echoid-s1164" xml:space="preserve">igitur inuertendo C A ad A B maiorem proportionem habebit quàm
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            H D ad D E.</s>
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          </p>
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        <div xml:id="echoid-div70" type="section" level="1" n="44">
          <head xml:id="echoid-head69" xml:space="preserve">LEMMA III.</head>
          <p style="it">
            <s xml:id="echoid-s1166" xml:space="preserve">Si quatuor quantitates eandem rationem habuerint homologorum ſum-
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            mæ, vel differentiæ in eadem ratione erunt.</s>
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          <p style="it">
            <s xml:id="echoid-s1168" xml:space="preserve">OStenſum enim fuit in elemen-
              <lb/>
              <figure xlink:label="fig-0053-01" xlink:href="fig-0053-01a" number="23">
                <image file="0053-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0053-01"/>
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            tis, quod proportionalium om-
              <lb/>
            nes antecedentes ad omnes conſequen-
              <lb/>
            tes eandem proportionem habent,
              <lb/>
            quàm vna antecedentium ad vnam
              <lb/>
            conſequentium. </s>
            <s xml:id="echoid-s1169" xml:space="preserve">Similiter oſtenſum
              <lb/>
            fuit, quod ſi totum ad totum eandem
              <lb/>
            rationem habuerit, quàm ablatum
              <lb/>
            ad ablatum, & </s>
            <s xml:id="echoid-s1170" xml:space="preserve">reliquum ad reliquũ,
              <lb/>
            vt totum ad totum ſe habebit; </s>
            <s xml:id="echoid-s1171" xml:space="preserve">ſed
              <lb/>
            vno verbo homologorum ſummæ, vel
              <lb/>
            differentiæ in eadem ratione erunt
              <lb/>
            iuxtà Arabici expoſitoris compendium.</s>
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          <head xml:id="echoid-head70" xml:space="preserve">LEMMA IV.</head>
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            <s xml:id="echoid-s1173" xml:space="preserve">Si prima A B ad ſecundam D E maiorem proportionem habuerit,
              <lb/>
            quàm tertia B C ad qnartam E H: </s>
            <s xml:id="echoid-s1174" xml:space="preserve">dico, quod comparando homologorum
              <lb/>
            ſummas A B ad D E maiorem proportionem habebit, quàm prima cum
              <lb/>
            tertia, ideſt A C ad ſecundam cum quarta, ideſt D H.</s>
            <s xml:id="echoid-s1175" xml:space="preserve"/>
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            <s xml:id="echoid-s1176" xml:space="preserve">FIat B F ad E H, vt A B ad D E: </s>
            <s xml:id="echoid-s1177" xml:space="preserve">ergo A B ad D E eſt, vt A F ad D H; </s>
            <s xml:id="echoid-s1178" xml:space="preserve">ſed
              <lb/>
              <note position="right" xlink:label="note-0053-01" xlink:href="note-0053-01a" xml:space="preserve">Lem. 3.</note>
            A F maior eſt quàm A C, igitur A F ad eandem D H maiorem proportio-
              <lb/>
            nem habet, quàm A C: </s>
            <s xml:id="echoid-s1179" xml:space="preserve">& </s>
            <s xml:id="echoid-s1180" xml:space="preserve">ideo A B ad D E maiorem proportionem habet, quàm
              <lb/>
            A C ad D H.</s>
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            <s xml:id="echoid-s1182" xml:space="preserve">Secundò ijſdem poſitis, dico, quod tertia B C ad quartam E H minorem pro-
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            portionem habet quàm A C ad D H.</s>
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          <p style="it">
            <s xml:id="echoid-s1184" xml:space="preserve">Fiat vt B C ad E H, ita I B ad D E, ergo C B ad E H eſt, vt C I ad H D;
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            </s>
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              <note position="right" xlink:label="note-0053-02" xlink:href="note-0053-02a" xml:space="preserve">Ibidem.</note>
            ſed A B maior eſt quàm I B, & </s>
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            <s xml:id="echoid-s1187" xml:space="preserve">igitur I C ad </s>
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